Multiresolution stochastic simulations of reaction–diffusion processes

Abstract

Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by many-particle systems. The proposed method quantifies and efficiently handles the associated stiffness in simulating the system dynamics and its computational efficiency and accuracy are demonstrated in simulations of a model problem described by the Fisher-Kolmogorov equation. The method is general and can be applied to other many-particle models of physical processes. Please check this proof carefully. Our staff will not read it in detail after you have returned it. Translation errors between word-processor files and typesetting systems can occur so the whole proof needs to be read. Please pay particular attention to: tabulated material; equations; numerical data; figures and graphics; and references. If you have not already indicated the corresponding author(s) please mark their name(s) with an asterisk. Please e-mail a list of corrections or the PDF with electronic notes attached --do not change the text within the PDF file or send a revised manuscript.Please bear in mind that minor layout improvements, e.g. in line breaking, table widths and graphic placement, are routinely applied to the final version.Please note that, in the typefaces we use, an italic vee looks like this: n, and a Greek nu looks like this: n.We will publish articles on the web as soon as possible after receiving your corrections; no late corrections will be made.Please return your final corrections, where possible within 48 hours of receipt, by e-mail to: proofs@rsc.org Reprints-Electronic (PDF) reprints will be provided free of charge to the corresponding author. Enquiries about purchasing paper reprints should be addressed via: http://www.rsc.org/Publishing/ReSourCe/PaperReprints/. Costs for reprints are below: Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by many-particle systems. The proposed method quantifies and efficiently handles the associated stiffness in simulating the system dynamics and its computational efficiency and accuracy are demonstrated in simulations of a model problem described by the Fisher-Kolmogorov equation. The method is general and can be applied to other many-particle mod...

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